1. What is meant by operations in mathematics? or Math 30-11

2. 2

3. Have I seen operations on functions before?? quadratic linear constant linear New functions can be formed by performing operations with functions. Math 30-13

4. Basic Function Operations Sum Difference Product Quotient Restrictions or NPV’s are functions that exist and are defined over a domain. Math 30-14 Linear Quadratic Radical linear Rational monomial, binomial Absolute Value first degree Cubic Exponential Logarithmic

5. The sum f + g To find the sum of two functions, add them together. Simplify by combining like terms. Algebraically New function Math 30-15

6. Graphing with technology Math 30-16

7. The difference f - g To find the difference between two functions, subtract the second from the first. Simplify by combining like terms. Algebraically New function Math 30-17

8. Sketch the graph using technology and determine the domain and range. Math 30-18

9. (f + g - h)(x) Given f(x) = 2x + 6, g(x) = -4x - 3, and write an expression in simplest form and determine domain and range. = f(x) + g(x) - h(x) = (2x + 6) + (-4x - 3) - = -2x + 3 - How does the domain of each individual function affect the domain of the new function? Math 30-19

10. The domain of h(x) is the sum of the domains of f(x) and g(x) The range of h(x) is the sum of the ranges of f(x) and g(x) The domain of h(x) is the overlap of the domains of f(x) and g(x) Determine the range graphically or use substitution. Math 30-110

11. Sketch the Graph of the sum f + g Consider the functions What part of the graphs would be added? x-coordinates? y-coordinates? Domain Range Math 30-111

12. 10.1 Sums and Differences http://www.psja.k12.tx.us/~abcron/GeoGebraM enu/GeogebraFiles/arithmetic/add_funct.html http://www.psja.k12.tx.us/~abcron/GeoGebraM enu/GeogebraFiles/arithmetic/sub_funct.html Math 30-112

13. Sketch a graph of the difference of f(x) and g(x). Use your knowledge of transformations to verify the graph. Domain Range Math 30-113

14. Consider Domain: Range: Is the Domain ofthe sum of the two domains? Is the Range ofthe sum of the two ranges? Math 30-114

15. Consider and. Express the sum h(x) = (f + g)(x) in simplest form and state the domain and range. Math 30-115

16. To sketch the graph of a sum of two functions given their graphs, ______ the ____coordinates at each x-value. add y To sketch the graph of a difference of two functions given their graphs, __________ the ____coordinates at each x-value. subtract y The domain of f(x) + g(x) is the overlap (intersection) of the domains of the individual functions. The range of f(x) + g(x) is determined from the graph of the sum or difference. Math 30-116

17. Page 483 1a,c,d, 2c,d, 4a,b, 5, 6, 7, 8, 9c,d, 10(new), 11a,b, 13, 14, C1, C2 Math 30-117

18. http://www.intmath.com/functions-and- graphs/2a-domain-and-range.php Domain and Range Review http://www.mathsisfun.com/sets/functions- operations.html http://www.wtamu.edu/academic/anns/mps/mat h/mathlab/col_algebra/col_alg_tut30b_operatio ns.htm Operations with Functions Math 30-118